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On the holomorphic solution of nonlinear totally characteristic equations with several space variables. (English) Zbl 1003.35005
Summary: The authors study a class of nonlinear singular partial differential equations of the type \(t\partial_t u=F(t,x,u, \nabla_xu)\) in the complex domain \(\mathbb{C}_t\times C_x^n\). Under certain assumptions, they prove the existence and uniqueness of holomorphic solution near the origin of \(\mathbb{C}_t \times \mathbb{C}^n_x\).

MSC:
35A07 Local existence and uniqueness theorems (PDE) (MSC2000)
35A10 Cauchy-Kovalevskaya theorems
35A20 Analyticity in context of PDEs
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